The given data points from the graph of the exponential function, f, and the, values from the table of the function g, gives the statement that correctly compares the two functions as the option;
B. They have the same x–intercept but different end behaviours as x approaches ∞What is the end behaviour of a graph?The end behaviour of a function is the description of how the function behaves towards the boundaries of the x–axis.
The given points on the exponential function, f, are;
(-0.25, 10), (0, 6), (5, -2) and also the x–intercept (1, 0)
The points on the function g, obtained from the table of the values for g(x), expressed as ordered pairs are;
(-1, 15), (0, 3), (1, 0), (2, -34), (3, -16)
The coordinates of the x–intercept is given by the point where the y–value is zero.
The x–intercept for the exponential function, f, is therefore (1, 0)
Similarly, the x–intercept for the function, g, is (1, 0)
Therefore, both functions have the same x–intercept
However, the end behaviour of the function, f, as the x approaches infinity is that f(x) approaches negative infinity, while the end behaviour of the function, g, as the the value of x approaches infinity is g(x) is increasing towards positive infinity.
The correct option is therefore;
B. They have the same x–intercept but different end behaviour as x approaches ∞Learn more about the end behaviour of a function here:
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Finding the final amount in a word problem on continuous exponential growth or decay
Given:
The mass of radioactive follows an exponential decay model
The initial mass = 418 kg
Decreases at a rate = r = 4% per day
So, the general formula for the mass will be:
[tex]m=418\cdot(1-0.04)^d[/tex]where: (m) is the mass after (d) days
So, to find the mass after 2 days, we will substitute with d = 2
so,
[tex]m=418\cdot(1-0.04)^2=418\cdot0.96^2=385.2288[/tex]rounding to the nearest tenth
so, the answer will be mass after 2 days = 385.2 kg
Shown in the equation are the steps a student took to solve the simple interest formula A=P(1+rt) for r
Given:
We're given the steps a student took to solve the simple interest formula.
To find:
The algebraic error in student's work.
Step-by-step solution:
Let us first solve the equation and then we will spot the error in the solution:
A = P(1 + rt)
A = p + prt
A - p = prt
A - p / pt = r
Upon comparing both solutions, we can clearly see that the student made a mistake in the second step in the multiplication process.
The student should write A = p + prt in the second step in place of
A = p + rt, because p is multiplied with the whole bracket.
In scalene triangle ABC shown in the diagram below, m2C = 90°.B.Which equation is always true?sn A = sin Bcos sn A = cos BCanAB4 5 678 9 1011
inNote: To know which equation is true, then we will have to TEST for each of the choices we are to pick from.
From the tirangle in the image.
[tex]\begin{gathered} 1)\sin \text{ A =}\frac{\text{ Opp}}{\text{Hyp}}\text{ = }\frac{a}{c} \\ \cos \text{ B = }\frac{\text{ADJ}}{\text{HYP}}\text{ = }\frac{a}{c} \\ So\text{ from the above, we can s}ee\text{ that: SinA = Cos B :This mean the choice are equal} \\ \end{gathered}[/tex][tex]\begin{gathered} 2)\text{ To test for the second choice we have..} \\ \text{ Cos A = Cos B} \\ \text{for Cos A =}\frac{\text{Adj}}{\text{Hyp}}\text{ =}\frac{b}{c} \\ \\ \text{for Cos B = }\frac{Adj}{\text{Hyp}}\text{ = }\frac{a}{c} \\ \text{from here we can s}ee\text{ that Cos A }\ne\text{ Cos B : meaning Cos A is not equal to Cos B} \\ \end{gathered}[/tex]3) To test for the third choice: Sin A = Cos A
[tex]\begin{gathered} \sin \text{ A=}\frac{opp}{\text{Hyp}}\text{ = }\frac{a}{c} \\ \cos \text{ A = }\frac{Adj}{\text{Hyp}}\text{ = }\frac{b}{c} \\ we\text{ can s}ee\text{ that sinA }\ne\text{ cos }A,\text{ This mean they are not equal} \end{gathered}[/tex][tex]\begin{gathered} 4)\text{ To test if: tan A = sin B} \\ \text{ }tan\text{ A = }\frac{opp}{\text{Adj}}\text{ = }\frac{a}{b} \\ \\ \text{ sin B = }\frac{Opp}{\text{Hyp}}\text{ = }\frac{b}{c} \\ so\text{ from what we have, w can s}ee\text{ that tan A }\ne\text{ sinB: Meaning they are not equal.} \end{gathered}[/tex]Meaning the first choice is the answer that is sin A = CosB
to rent a van a moving company charges $40.00 plus $0.50per miles
The problem talks about the cost for renting a van, which can be calculated adding $40.00 plus $0.50 for each mile.
The problem asks to wirte an explicit equation in slope-intercept form which can represent the cost of renting a van depending on the amount of miles. Then, the problem asks to find the cost if you drove 250 miles.
suppose that the amount of time it takes to build a highway vadies directly with the length of the highway and inversely with the number of workers. suppose also that it takes 300 workers 22 week to build 24 miles of highway. how long will it take 225 to build 27 miles of highway
What is the APY for money invested at each rate?(A) 14% compounded semiannually(B) 13% compounded continuously
APY means Annual Percentage Yield
The APY is given by the formula:
[tex]\text{APY}=\lbrack(1+\frac{r}{n}\rbrack^n-1[/tex]where r is the rate (in decimals)
n is the number of times the interest was compounded
A) For the money invested at 14% compounded semiannually
r = 14% = 14/100
r = 0.14
n = 2
Substitute n = 2, r = 0.14
[tex]\begin{gathered} \text{APY = \lbrack{}1+}\frac{0.14}{2}\rbrack^2-1 \\ \text{APY}=\lbrack1+0.07\rbrack^2-1 \\ \text{APY}=\lbrack1.07\rbrack^2-1 \\ \text{APY}=0.1449 \\ \text{APY}=0.1449\times100\text{ \%} \\ \text{APY}=14.49\text{ \%} \end{gathered}[/tex]B) For the money invested at 13% compounded continuously
How long will it take for an investment of 2900 dollars to grow to 6800 dollars, if the nominal rate of interest is 4.2 percent compounded quarterly? FV = PV(1 + r/n)^ntAnswer = ____years. (Be sure to give 4 decimal places of accuracy.)
ANSWER :
The answer is 20.3971 years
EXPLANATION :
The compounding interest formula is :
[tex]FV=PV(1+\frac{r}{n})^{nt}[/tex]where :
FV = future value ($6800)
PV = present value ($2900)
r = rate of interest (4.2% or 0.042)
n = number of compounding in a year (4 : compounded quarterly)
t = time in years
Using the formula above :
[tex]6800=2900(1+\frac{0.042}{4})^{4t}[/tex]Solve for t :
[tex]\begin{gathered} \frac{6800}{2900}=(1.0105)^{4t} \\ \text{ take ln of both sides :} \\ \ln(\frac{6800}{2900})=\ln(1.0105)^{4t} \\ \operatorname{\ln}(\frac{6800}{2900})=4t\operatorname{\ln}(1.0105) \\ 4t=\frac{\ln(\frac{6800}{2900})}{\ln(1.0105)} \\ t=\frac{\ln(\frac{6800}{2900})}{4\ln(1.0105)} \\ t=20.3971 \end{gathered}[/tex]24) The radius of a circle is 6 inches. What is the area of a sector that has a central angle of 100 degrees 
Answer
Area of the sector = 31.42 square inches
Explanation
The area of a sector that has a central angle, θ, in a circle of radius r, is given as
[tex]\begin{gathered} \text{Area of a sector = }\frac{\theta}{360\degree}\times(Area\text{ of a circle)} \\ \text{Area of a circle =}\pi\times r^2 \\ \text{Area of a sector = }\frac{θ}{360°}\times\pi\times r^2 \end{gathered}[/tex]For this question,
θ = central angle = 100°
π = pi = 3.142
r = radius = 6 inches
[tex]\begin{gathered} \text{Area of a sector = }\frac{θ}{360°}\times\pi\times r^2 \\ \text{Area of a sector = }\frac{100\degree}{360\degree}\times3.142\times6^2=31.42\text{ square inches} \end{gathered}[/tex]Hope this Helps!!!
Plot the point given by the following polar coordinates on the graph below. Each circular grid line is 0.5 units apart.230(2.5. -,
Solution:
Given:
[tex](2.5,-\frac{2\pi}{3})[/tex]In a charity triathlon, Mark ran half the distance and swam a quarter of the distance when he took a quick break to get a drink of Gatorade he was just starting to bite the remaining 12 miles what was the total distance of the race?
Sydney is making bracelets, 3 bracelets require 21 beads. The number of braclets varies directly with the number of beads.
Write an equation in the form of y = ax then find the amount o
beads needed for 32 bracelets.
Step-by-step explanation:
"varies DIRECTLY with" means there is an y = ax relationship.
y = number of bracelets
x = number of beads
3 = a×21
a = 3/21 = 1/7
now, when we have 32 bracelets
32 = 1/7 × x
32×7 = x = 224
224 beads are needed for 32 bracelets.
the drop down menus choices are: two imaginary solutionstwo real solutionsone real solution
Given a quadratic equation of the form:
[tex]ax^2+bx+c=0[/tex]The discriminant is:
[tex]D=b^2-4ac[/tex]And we can know the number of solutions with the value of the discriminant:
• If D < 0, the equation has 2 imaginary solutions.
,• If D = 0, the equation has 1 real solution
,• If D > 0, the equation has 2 real solutions.
Equation One:
[tex]x^2-4x+4=0[/tex]Then, we calculate the discriminant:
[tex]D=(-4)^2^-4\cdot1\cdot4=16-16=0[/tex]D = 0
There are 1 real solution.
Equation Two:
[tex]-5x^2+8x-9=0[/tex]
Calculate the discriminant:
[tex]D=8^2-4\cdot(-5)\cdot(-9)=64-20\cdot9=64-180=-116[/tex]D = -116
There are 2 imaginary solutions.
Equation Three:
[tex]7x^2+4x-3=0[/tex]
Calculate the discriminant:
[tex]D=4^2-4\cdot7\cdot(-3)=16+28\cdot3=16+84=100[/tex]D = 100
There are 2 real solutions.
Answers:
Equation 1: D = 0, One real solution.
Equation 2: D = -116, Two imaginary solutions.
Equation 3: D = 100, Two real solutions.
How far is the bottom of the ladder from thebottom of the wall? Use the PythagoreanTheorem to determine the solution. Explain howyou found your answer.
The Pythagorean Theorem is
[tex]c^2=a^2+b^2[/tex]where
c=hypotenuse=13
a=12
b=x
then we substitute the values
[tex]13^2=12^2+x^2[/tex]then we isolate the x
[tex]\begin{gathered} x=\sqrt[]{13^2-12^2} \\ x=\sqrt[]{169-144} \\ x=\sqrt[]{25} \\ x=5 \end{gathered}[/tex]The bottom of the ladder is 5m far from the bottom of the wall
Solve graphically by the intersection method. Give the solution in interval notation.5x+2<2x−4
The green line represents 5x + 2
The purple line represents 2x - 4
The orange-colour line represents the intersection of the lines above, which is the solution to the inequality:
5x + 2 < 2x - 4
The intersection is represented by a broken line, to signify the strict < in the equation
Carrie sold 112 boxes of cookies, Megan sold 126 boxes of cookies, Julie sold 202 boxes of cookies, and Ashton sold 176 boxes of cookies. what was the average number of boxes of cookies sold by each individual
Answer:
154 boxes.
Explanation:
To calculate the average number of boxes of cookies sold by each individual, we use the formula:
[tex]\text{Average=}\frac{\text{Sum of all boxes sold}}{\text{Number of individuals}}[/tex]This gives:
[tex]\begin{gathered} \text{Average}=\frac{112+126+202+176}{4} \\ =\frac{616}{4} \\ =154\text{ boxes} \end{gathered}[/tex]The average number of boxes of cookies sold by each individual was 154 boxes.
Solve the system withelimination.1-2x + y = 813x + y = -2([?],[?]
Now we substitute the value of x into the first equation to get the value of y
[tex]\begin{gathered} -2\cdot-2+y=8 \\ 4+y=8 \\ y=8-4=4 \end{gathered}[/tex]Finally the solution is (-2,4)
Graph the line with the given slope m and y-intercept b.
m = 4,b=-5
The graph of the linear equation can be seen in the image at the end.
How to graph the linear equation?
The general linear equation is.
y = m*x + b
Where m is the slope and b is the y-intercept.
Here we know that m = 4 and b = -5, so we have:
y = 4*x - 5
To graph this line, we need to find two points.
Evaluating in x = 0 we get:
y = 4*0 - 5 = -5
Evaluating in x = 2 we get:
y = 4*2 - 5 = 8 - 5 = 3
So we have the points (0, -5) and (2, 3), so now we need to graph these points and connect them with a line, the graph can be seen below:
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12"retest: CirclesOASelect the correct answerArc XY located on circle A has a length of 40 centimeters. The radius of the circle is 10 centimeters. What is the measure of the correspondingcentral angle for XY in radians?O B.OC.OD. 34TResetSubmit TestNextReader Tools
step 1
Find out the circumference
[tex]C=2\pi r[/tex]where
r=10 cm
substitute
[tex]\begin{gathered} C=2\pi(10) \\ C=20\pi\text{ cm} \end{gathered}[/tex]Remember that
The circumference subtends a central angle of 2pi radians
so
Applying proportion
Find out the central angle by an arc length of 40 cm
[tex]\begin{gathered} \frac{2\pi}{20\pi}=\frac{x}{40} \\ \\ x=4\text{ rad} \end{gathered}[/tex]therefore
The answer is 4 radians Option BUnit 6 lesson3 plsss help
From the triangles ∠ABC ≅ ∠MNP.
Given we have two triangles ABC and PNM
Both triangles have same shape but different angles.
we need to find ∠ABC ≅ ?
we can notice that :
∠A ≅ ∠M
∠B ≅ ∠N
∠C ≅ ∠P
hence these angles are similar to each other.
So, ∠ABC ≅ ∠MNP.
Hence we get the answer as ∠ABC ≅ ∠MNP.
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Find the volume of a cone with a height of 10cm and diameter of 6cm. Round to the nearest tenth. Use 3.14 for .
We can find the volume of a cone using the formula
[tex]V=\frac{\pi r^2h}{3}[/tex]Where
h = height
r = radius
Remember that
[tex]d=2r\Rightarrow r=\frac{d}{2}[/tex]Therefore, let's find out the radius first, the problem says that the diameter is 6cm, then
[tex]r=\frac{6}{2}=3\text{ cm}[/tex]The radius is 3cm and the height is 10cm, let's use it in our formula:
[tex]\begin{gathered} V=\frac{\pi\cdot(3)^2\cdot10}{3} \\ \\ V=30\pi \end{gathered}[/tex]The problem also say to use = 3.14, then the volume is
[tex]\begin{gathered} V=30\cdot3.14 \\ V=94.2 \end{gathered}[/tex]Therefore, the volume is
[tex]V=94.2\text{ cm}^3[/tex]
I’ve done all the other parts, I simply need you to graph the proabola!
Given
[tex]y=x^2-4x+3[/tex]Find
Graph the parabola of the given function
Explanation
[tex]y=x^2-4x+3[/tex]solve the equation
[tex]\begin{gathered} x^2-4x+3=0 \\ x^2-3x-x+3=0 \\ x(x-3)-(x-3)=0 \\ (x-1)(x-3)=0 \\ x=1,3 \end{gathered}[/tex]vertex can be found by using the formula,
[tex]-\frac{b}{2a}=-\frac{-4}{2}=2[/tex]x = 2 , substitute this in equation to get y value,
y = -1
if x = 0 then y =3 and if y= 0 then x = 1, 3
Final Answer
A = P + PRT/100Make P the subject from the formula.
ANSWER
[tex]P=\frac{100A}{100+RT}[/tex]EXPLANATION
We want to make the subject of the formula in the given equation:
[tex]A=P+\frac{PRT}{100}[/tex]First, factorize the right-hand side of the equation:
[tex]A=P(1+\frac{RT}{100})[/tex]Simplify the bracket:
[tex]A=P(\frac{100+RT}{100})[/tex]Now, divide both sides by the term in the bracket:
[tex]\begin{gathered} \Rightarrow P=A\cdot\frac{100}{100+RT} \\ \Rightarrow P=\frac{100A}{100+RT} \end{gathered}[/tex]That is the answer.
What is the equation of a line with slope 7/12 and y-intercept -3?
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m represents slope
c represents y intercept
Given that m = 7/12 and c = - 3, the equation of the line would be
y = 7x/12 - 3
Determine whether the graph shown is the graph of a polynomial function
the given graph is smooth and its domain is containing all real numbers
so it is a polynomial function.
In Square ABCD, AE = 3x + 5 and BD = 10x + 2.What is the length of AC?
Let's begin by identifying key information given to us:
We have square ABCD
[tex]\begin{gathered} AE=3x+5 \\ BD=10x+2 \\ BD=2\cdot AE \\ 10x+2=2(3x+5) \\ 10x+2=6x+10 \\ \text{Put like terms together, we have:} \\ 10x-6x=10-2 \\ 4x=8 \\ \text{Divide both sides by ''4'', we have:} \\ \frac{4x}{4}=\frac{8}{4} \\ x=2 \\ \\ \end{gathered}[/tex]For a square, the diagonals are equal, AC = BD
[tex]\begin{gathered} AC=BD \\ AC=10x+2 \\ x=2 \\ AC=10(2)+2=20+2 \\ AC=22 \end{gathered}[/tex]help meeeeeeeeee pleaseee !!!!!
The values of the functions are:
a. (f + g)(x) = x² + 3x + 5
b. (f - g)(x) = x² - 3x + 5
c. (f * g)(x) = 3x³ + 15x
d. (f/g)(x) = (x² + 5)/3x.
How to Determine the Value of a Given Function?For any given function, we can evaluate the function by plugging in the equation of each of the functions in the given expression.
Thus, we have the following given functions:
f(x) = x² + 5
g(x) = 3x
a. Find the value of the function for the expression (f + g)(x).
We are required here to add the expression for each of the functions, f(x) and g(x) together, which is:
(f + g)(x) = (x² + 5) + (3x)
(f + g)(x) = x² + 3x + 5
b. Evaluate (f - g)(x) by subtracting the function g(x) from f(x):
(f - g)(x) = (x² + 5) - (3x)
(f - g)(x) = x² - 3x + 5
c. Find (f * g)(x):
(f * g)(x) = (x² + 5) * (3x)
(f * g)(x) = x²(3x) + 5(3x)
(f * g)(x) = 3x³ + 15x
d. Find (f/g)(x):
(f/g)(x) = (x² + 5)/3x
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Describe the two different methods shown for writing the complex expression in standard form. Which method do you prefer? Explain
The first method simlpy executes the distributive property of multiplication over addition, and the definition of the imaginary number, i.
The second method factored out 4i first then perform the operation on the terms left inside the parenthesis , then executes the distributive property of multiplication over addition and the definition of the imaginary number, i.
I prefer the first method . It's simple and straight forward,
3. Jeremy asked a sample of 40 8th grade students whether or not they had a curfew. He then asked if they had a set bedtime for school nights. He recorded his data in this two-way frequency table. Bedtime 21 Curfew No Curfew Total No Bedtime Total 4 25 12 16 40 3 15 24 a. What percentage of students surveyed have a bed time but no curfew?
40 students (the total) represents 100%
To find what percentage represents 3 students (number of students with bedtime but no curfew), we can use the next proportion:
[tex]\frac{40\text{ students}}{3\text{ students}}=\frac{100\text{ \%}}{x\text{ \%}}[/tex]Solving for x,
[tex]\begin{gathered} 40\cdot x=100\cdot3 \\ x=\frac{300}{40} \\ x=7.5\text{ \%} \end{gathered}[/tex]Determine the value of x Round results to an appropriate number of significant digits
Given
Find
The value of x.
Explanation
length of AB = 22 - 3 = 19
using the trignometric ratios , we have
[tex]\begin{gathered} \sin13\degree=\frac{BD}{AB} \\ \sin13\degree=\frac{\frac{x}{2}}{19} \\ \sin13\degree\times38=x \\ 8.548=x \end{gathered}[/tex]Final Answer
Therefore , the length of x is 8.548
In ABC, B = 51°, b = 35, and a = 36. What are the two possible values for angle A to the nearest tenth of a degree?Select both correct answers.
Using the law of sines:
[tex]\frac{a}{\sin(A)}=\frac{b}{\sin (B)}[/tex]Solve for A using the data provided:
[tex]\begin{gathered} \sin (A)=\frac{\sin (B)\cdot a}{b} \\ A=\sin ^{-1}(\frac{\sin (51)36}{35}) \\ A\approx53.1 \\ or \\ A\approx126.9 \end{gathered}[/tex]